|
Definition
A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes).Lyons, John. "Semantics, vol. I." Cambridge: Cambridge (1977). p.158 and on. Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions. In mathematics, a definition is used to give a precise meaning to a new term, by describing a condition which unambiguously qualifies what a mathematical term is and is not. Definitions and axioms form the basis on which all of modern mathematics is to be constructed. Basic terminology In modern usage, a definition is something, typically expressed in words, that at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intensional Definition
In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give meaning or denotation to a term. Intensional definition An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. In the case of nouns, this is equivalent to specifying the properties that an object needs to have in order to be counted as a referent of the term. For example, an intensional definition of the word "bachelor" is "unmarried man". This definition is valid because being an unmarried man is both a necessary condition and a sufficient condition for being a bachelor: it is necessary because one cannot be a bachelor without being an unmarried man, and it is sufficient because any unmarried man is a bachelor.Cook, Roy T. "Intensional Definition". In ''A Dictionary of Philosophical Logic''. Edinburgh: Edinburgh University Press, 2009. 155. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set (mathematics)
A set is the mathematical model for a collection of different things; a set contains ''elements'' or ''members'', which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous foundations for all branches of mathematics since the first half of the 20th century. History The concept of a set emerged in mathematics at the end of the 19th century. The German word for set, ''Menge'', was coined by Bernard Bolzano in his work '' Paradoxes of the Infinite''. Georg Cantor, one of the founders of set theory, gave the following ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ostensive Definition
An ostensive definition conveys the meaning of a term by pointing out examples. This type of definition is often used where the term is difficult to define verbally, either because the words will not be understood (as with children and new speakers of a language) or because of the nature of the term (such as colors or sensations). It is usually accompanied with a gesture pointing to the object serving as an example, and for this reason is also often referred to as " definition by pointing". Overview An ostensive definition assumes the questioner has sufficient understanding to recognize the type of information being given. Ludwig Wittgenstein writes: So one might say: the ostensive definition explains the use—the meaning—of the word when the overall role of the word in language is clear. Thus if I know that someone means to explain a colour-word to me the ostensive definition "That is called 'sepia' " will help me to understand the word.... One has already to know (or be abl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of philosophy within the Lyceum (classical), Lyceum and the wider Aristotelianism, Aristotelian tradition. His writings cover many subjects including Physics (Aristotle), physics, biology, zoology, metaphysics, logic, ethics, aesthetics, Poetics (Aristotle), poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, meteorology, History of geology, geology, and government. Aristotle provided a complex synthesis of the various philosophies existing prior to him. It was above all from his teachings that Western culture, the West inherited its intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word
A word is a basic element of language that carries an objective or practical meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no consensus among linguists on its definition and numerous attempts to find specific criteria of the concept remain controversial. Different standards have been proposed, depending on the theoretical background and descriptive context; these do not converge on a single definition. Some specific definitions of the term "word" are employed to convey its different meanings at different levels of description, for example based on phonological, grammatical or orthographic basis. Others suggest that the concept is simply a convention used in everyday situations. The concept of "word" is distinguished from that of a morpheme, which is the smallest unit of language that has a meaning, even if it cannot stand on its own. Words are made out of at least on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seven Deadly Sins
The seven deadly sins, also known as the capital vices or cardinal sins, is a grouping and classification of vices within Christian teachings. Although they are not directly mentioned in the Bible, there are parallels with the seven things God is said to hate in the Book of Proverbs. Behaviours or habits are classified under this category if they directly give rise to other immoralities. According to the standard list, they are pride, greed, wrath, envy, lust, gluttony and sloth, which are contrary to the seven capital virtues. This classification originated with the Desert Fathers, especially Evagrius Ponticus. Evagrius' pupil John Cassian with his book ''The Institutes'' brought the classification to Europe, where it became fundamental to Catholic confessional practices as documented in penitential manuals, sermons such as " The Parson's Tale" from Chaucer's '' Canterbury Tales'' and artworks such as Dante's ''Purgatory'' where the penitents of Mount Purgatory are gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Posterior Analytics
The ''Posterior Analytics'' ( grc-gre, Ἀναλυτικὰ Ὕστερα; la, Analytica Posteriora) is a text from Aristotle's ''Organon'' that deals with demonstration, definition, and scientific knowledge. The demonstration is distinguished as ''a syllogism productive of scientific knowledge'', while the definition marked as ''the statement of a thing's nature, ... a statement of the meaning of the name, or of an equivalent nominal formula''. Content In the '' Prior Analytics'', syllogistic logic is considered in its formal aspect; in the ''Posterior'' it is considered in respect of its matter. The "form" of a syllogism lies in the necessary connection between the premises and the conclusion. Even where there is no fault in the form, there may be in the matter, i.e. the propositions of which it is composed, which may be true or false, probable or improbable. When the premises are certain, true, and primary, and the conclusion formally follows from them, this is demonstrat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enumerative Definition
An enumerative definition of a concept or term is a special type of extensional definition that gives an explicit and exhaustive listing of all the objects that fall under the concept or term in question. Enumerative definitions are only possible for finite sets and only practical for relatively small sets. An example of an enumerative definition for the set ; extant monotreme species (for which the intensional definition is ''species of currently-living mammals that lay eggs'') would be : platypuses : echidnae: :: short-beaked echidna :: long-beaked echidnae: ::: Sir David's long-beaked echidna ::: eastern long-beaked echidna ::: western long-beaked echidna See also * Definition * Extension * Extensional definition In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give meaning or denotation to a term. Intensional definition An intensional definition gives ... * Se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Object (philosophy)
An object is a philosophical term often used in contrast to the term ''subject''. A subject is an observer and an object is a thing observed. For modern philosophers like Descartes, consciousness is a state of cognition that includes the subject—which can never be doubted as only it can be the one who doubts—and some object(s) that may be considered as not having real or full existence or value independent of the subject who observes it. Metaphysical frameworks also differ in whether they consider objects existing independently of their properties and, if so, in what way. The pragmatist Charles S. Peirce defines the broad notion of an object as anything that we can think or talk about. In a general sense it is any entity: the pyramids, gods, Socrates, Alpha Centauri, the number seven, a disbelief in predestination or the fear of cats. In a strict sense it refers to any definite being. A related notion is objecthood. Objecthood is the state of being an object. One app ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homonyms
In linguistics, homonyms are words which are homographs (words that share the same spelling, regardless of pronunciation), or homophones ( equivocal words, that share the same pronunciation, regardless of spelling), or both. Using this definition, the words ''row'' (propel with oars), ''row'' (a linear arrangement) and ''row'' (an argument) are homonyms because they are homographs (though only the first two are homophones): so are the words ''see'' (vision) and ''sea'' (body of water), because they are homophones (though not homographs). A more restrictive and technical definition requires that homonyms be simultaneously homographs ''and'' homophoneshomonym ''Random House Unabridged Dictionary'' at dictionary.com – that is to say they have identical spelling ''and'' pronunciation, but with different meanings. Examples are the pair ''stalk' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> Word")
